A metal rod AB of length has its one end A in ice at , and the other end B in water at . If a point P on the rod is maintained at , then it is found that equal amounts of water and ice evaporate and melt per unit time. [2009]

Question

A metal rod AB of length $10 x$ has its one end A in ice at $0 ° C$ , and the other end B in water at $100 ° C$ . If a point P on the rod is maintained at $400 ° C$ , then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporation of water is $540 cal / g$ and latent heat of melting of ice is $80 cal / g$ . If the point P is at a distance of $λ x$ from the ice end A, find the value of $λ$ .

[Neglect any heat loss to the surrounding.] [2009]

Smart Achievers · Accepted Answer

(9)

$0 ° C$

$\frac{d Q_{1}}{d t} = L_{f} \frac{d m_{1}}{d t} = \frac{K A \cdot 400}{λ x} .....(i)$

$For heat flow from P to B$

$\frac{d Q_{2}}{d t} = L_{vap} \frac{d m_{2}}{d t} = \frac{K A \cdot 300}{10 x - λ x} .....(ii)$ $[Given \frac{d m_{1}}{d t} = \frac{d m_{2}}{d t}]$

Dividing eq. (i) by (ii) and solving we get $λ = 9$

Solution

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Solution

Ans. (9) For heat flow from P to O dQ1dt=Lfdm1dt=KA·400λx .....(i) For heat flow from P to B dQ2dt=Lvapdm2dt=KA·30010x-λx .....(ii) [Given dm1dt=dm2dt] Dividing eq. (i) by (ii) and solving we get λ=9

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